Relational Namespace

Core Definition

Relational frames foreground relations between entities, emphasizing the connections, associations, and dependencies that hold between two or more participants. These frames center on dyadic or polyadic structures where the relationship itself is the primary semantic content, rather than properties of individual entities or events occurring to them.

Theoretical foundation: Relational frames encode the basic template RELATION(x, y) or RELATION(x, y, z, ...), where entities stand in specific relationships to each other. Unlike monadic states (which describe properties of single entities) or events (which describe changes), relations describe how entities are connected or associated.

Key characteristics:

Multi-participant structure: Minimally two participants (dyadic), sometimes more (polyadic)
Relational predicate: The relation itself is profiled, not the entities
Asymmetric or symmetric: Relations may distinguish participant roles or treat them equivalently
Static/stative: Relations typically hold over time without internal change
No inherent endpoint: Relations obtain without natural termination (atelic)
Non-agentive: Relations hold between entities without volitional control

Vendler aspectual class: States (like other statives, but inherently relational)

Philosophical grounding: Relations connect to relational properties in metaphysics - properties that entities have in virtue of standing in relations to other entities. This includes possession, kinship, spatial configuration, part-whole structure, and abstract connections.

Relational Types: A Comprehensive Taxonomy

Relational frames exhibit diverse types based on what kind of connection or association they encode.

Possession Relations

Definition: Relations where one entity (possessor) has control over, ownership of, or association with another entity (possessed).

Semantic template: POSSESS(Possessor, Possessed)

Portuguese realization:

Primary verb: ter (have)
Emphatic: possuir (possess/own)
Copular: ser de (belong to)

Alienable Possession (Transferable)

Definition: Possession of entities that can be transferred, acquired, or lost without changing the possessor's essential nature.

Examples:

João tem um carro (João has a car)
- Possessor: João
- Possessed: carro (car)
- Alienable: car can be sold/transferred

Maria possui uma casa (Maria owns a house)
- Emphatic possession verb *possuir*
- Alienable ownership

Pedro tem muito dinheiro (Pedro has much money)
- Mass noun possessed (money)
- Highly alienable

Properties:

Can be acquired or lost
Typically material objects, money, property
Verb: ter (have) or possuir (own/possess)
Can be made explicit with copula: Este livro é meu (This book is mine)

Copular expression:

Este livro é meu (This book is mine)
A casa é de João (The house is João's)
- Uses *ser de* to express belonging
- Emphasizes ownership/belonging relation

Inalienable Possession (Non-transferable)

Definition: Possession of entities that cannot be transferred and are inherently associated with the possessor (body parts, kinship, inherent properties).

Examples:

João tem dois irmãos (João has two siblings)
- Kinship: inalienable relation
- Cannot transfer siblings

Maria tem cabelo preto (Maria has black hair)
- Body part: inalienable
- Part of person's physical makeup

A casa tem três quartos (The house has three rooms)
- Architectural part: integral component
- Cannot transfer rooms separately from house

Properties:

Cannot be transferred or sold
Typically body parts, kinship, inherent components
Verb: ter (have)
Reflects essential structure or inherent association

Possession Participant Structure

Asymmetric structure: Possessor and possessed have distinct roles

Possessor:

Typically animate (for alienable possession)
Can be inanimate (for part-whole: house has rooms)
Controller or bearer of possessed entity
Syntactic subject

Possessed:

Typically object or entity under control
Can be abstract (ideas, rights)
Syntactic direct object (with ter) or complement (with ser de)

Example analysis:

João tem um carro
[POSSESS(João[Possessor], carro[Possessed])]

Structure:
- João: Animate possessor, controller
- carro: Alienable possessed object
- Asymmetric: João ≠ carro in role

Kinship Relations

Definition: Relations based on family connections, including biological descent, marriage, and extended family ties.

Semantic template: KINSHIP(Relatum₁, KinshipType, Relatum₂)

Portuguese realization:

Primary copula: ser (be)
Indicates permanent/essential family relation

Examples:

João é pai de Maria (João is Maria's father)
- Relatum₁: João (father)
- Relatum₂: Maria (child)
- Kinship type: parent-child

Pedro é irmão de Ana (Pedro is Ana's brother)
- Relatum₁: Pedro
- Relatum₂: Ana
- Kinship type: sibling

Maria é avó de João (Maria is João's grandmother)
- Relatum₁: Maria (grandmother)
- Relatum₂: João (grandchild)
- Kinship type: grandparent-grandchild

Ana é casada com Pedro (Ana is married to Pedro)
- Relatum₁: Ana (spouse)
- Relatum₂: Pedro (spouse)
- Kinship type: marriage

Properties of Kinship Relations

1. Permanence: Marked with ser (permanent relation)

✓ João é pai de Maria (João is Maria's father - permanent)
✗ *João está pai de Maria (ungrammatical - cannot be temporary)

2. Symmetry patterns:

Symmetric kinship (same relation both directions):

Pedro é irmão de Ana ↔ Ana é irmã de Pedro
(Pedro is Ana's brother ↔ Ana is Pedro's sister)
- Same kinship type (sibling), gender-marked
- Symmetric structure

João é casado com Maria ↔ Maria é casada com João
(João is married to Maria ↔ Maria is married to João)
- Marriage: symmetric relation

Asymmetric kinship (different relations, complementary):

João é pai de Maria ↔ Maria é filha de João
(João is Maria's father ↔ Maria is João's daughter)
- Complementary pair: father ↔ daughter
- Asymmetric: different roles

Maria é avó de Pedro ↔ Pedro é neto de Maria
(Maria is Pedro's grandmother ↔ Pedro is Maria's grandson)
- Complementary pair: grandmother ↔ grandson

3. Transitivity (some kinship relations):

If: João é pai de Maria AND Maria é mãe de Pedro
Then: João é avô de Pedro
(Transitivity through generations)

4. Types of kinship:

Consanguineal (blood relation): pai (father), mãe (mother), irmão (brother)
Affinal (marriage): marido (husband), esposa (wife), sogro (father-in-law)
Extended: tio (uncle), primo (cousin), sobrinho (nephew)

Social and Professional Relations

Definition: Relations based on social roles, professional hierarchies, friendships, and institutional connections.

Semantic template: SOCIAL_RELATION(Relatum₁, RelationType, Relatum₂)

Portuguese realization: ser (be) for roles, ter (have) for some relations

Examples:

Professional/hierarchical:

João é professor de Maria (João is Maria's teacher)
- Professional role relation
- Hierarchical: teacher > student

O diretor é chefe dos funcionários (The director is the employees' boss)
- Institutional hierarchy
- Boss > employees

Maria é colega de João (Maria is João's colleague)
- Professional peer relation
- Symmetric (colleagues)

Social/friendship:

Pedro é amigo de Ana (Pedro is Ana's friend)
- Social bond: friendship
- Typically symmetric

João é conhecido de Maria (João is an acquaintance of Maria)
- Weak social tie
- Symmetric

Properties of Social/Professional Relations

1. Role-based structure:

Define participants by their social/professional roles
Often contextual (teacher-student relation holds in educational context)

2. Symmetry variation:

Symmetric social relations:

Pedro é amigo de Ana ↔ Ana é amiga de Pedro
(Friendship is symmetric)

João é colega de Maria ↔ Maria é colega de João
(Colleague relation is symmetric)

Asymmetric professional relations:

João é professor de Maria ≠ Maria é professora de João
(Teacher-student is asymmetric)

O diretor é chefe de João ≠ João é chefe do diretor
(Boss-subordinate is asymmetric)

3. Temporality:

Some social/professional relations can change
Use ser for current/general relation
Context determines if temporary or permanent

Part-Whole Relations (Meronymy)

Definition: Relations where one entity (part) is a component, member, or portion of another entity (whole).

Semantic template: PART_OF(Part, Whole) or HAS_PART(Whole, Part)

Portuguese realization:

ser parte de (be part of)
pertencer a (belong to)
ter (have - from whole's perspective)

Examples:

A roda é parte do carro (The wheel is part of the car)
- Part: roda (wheel)
- Whole: carro (car)
- Component-integral object

O dedo pertence à mão (The finger belongs to the hand)
- Part: dedo (finger)
- Whole: mão (hand)
- Body part meronymy

A cidade tem muitos bairros (The city has many neighborhoods)
- Whole: cidade (city)
- Parts: bairros (neighborhoods)
- Place-area relation

O livro tem dez capítulos (The book has ten chapters)
- Whole: livro (book)
- Parts: capítulos (chapters)
- Structural components

Types of Part-Whole Relations

Following Winston et al. (1987), part-whole relations exhibit several distinct types:

a) Component-Integral Object:

A roda é parte do carro (The wheel is part of the car)
O motor é componente do carro (The motor is a component of the car)
- Part is functional component of whole
- Removal affects whole's function
- Integral relationship

b) Member-Collection:

A árvore é parte da floresta (The tree is part of the forest)
João é membro do grupo (João is a member of the group)
- Individual member of collection
- Whole is collection of similar members
- Member-collective relation

c) Portion-Mass:

A fatia é parte do bolo (The slice is part of the cake)
Um copo de água (A glass of water - portion of water)
- Portion taken from mass
- Whole is homogeneous mass
- Quantitative extraction

d) Stuff-Object:

A madeira é o material da mesa (Wood is the material of the table)
A mesa é de madeira (The table is of wood)
- Material constitution
- Stuff composes object
- Material-object relation

e) Feature-Activity:

Pagar é parte de comprar (Paying is part of buying)
A assinatura é parte do contrato (Signing is part of the contract)
- Sub-activity of larger activity
- Feature of complex event
- Activity decomposition

f) Place-Area:

O bairro fica na cidade (The neighborhood is in the city)
A sala é parte da casa (The room is part of the house)
- Spatial part-whole
- Location-within-location
- Geographic containment

Properties of Part-Whole Relations

1. Asymmetry: Part-whole relations are inherently asymmetric

A roda é parte do carro (The wheel is part of the car)
≠ O carro é parte da roda (The car is part of the wheel)

2. Transitivity: Part-whole relations are transitive

If: O dedo é parte da mão AND A mão é parte do corpo
Then: O dedo é parte do corpo
(Finger is part of hand, hand is part of body → finger is part of body)

3. Proper parthood: Part is not identical to whole

A roda ≠ o carro (The wheel is not the car)
- Part is distinct from whole
- Whole has other parts besides the focal part

4. Essential vs. optional parts:

Essential parts: Remove them, whole ceases to function/exist properly
- O motor do carro (car's motor - essential)
Optional parts: Can be removed without destroying whole
- O espelho retrovisor (rearview mirror - less essential)

Quantitative and Measure Relations

Definition: Relations expressing measurements, quantities, dimensions, ages, values, or costs associated with entities.

Semantic template: MEASURE(Entity, Dimension, Value)

Portuguese realization:

ter (have) for age, dimensions
medir (measure) for dimensions
custar (cost) for value
pesar (weigh) for weight

Examples:

Age relations:

João tem 30 anos (João is 30 years old / João has 30 years)
- Entity: João
- Dimension: age
- Value: 30 anos (30 years)

A árvore tem 100 anos (The tree is 100 years old)

Dimension relations:

A mesa tem 2 metros de comprimento (The table is 2 meters long / has 2 meters of length)
- Entity: mesa (table)
- Dimension: comprimento (length)
- Value: 2 metros

A sala mede 20 metros quadrados (The room measures 20 square meters)
- Verb *medir* (measure)
- Dimension: area
- Value: 20 m²

A montanha tem 3000 metros de altura (The mountain is 3000 meters high)
- Dimension: altura (height)
- Value: 3000 metros

Value/cost relations:

O livro custa 50 reais (The book costs 50 reais)
- Entity: livro (book)
- Dimension: monetary value
- Value: 50 reais

O carro vale 50 mil reais (The car is worth 50 thousand reais)
- Verb *valer* (be worth)

Weight relations:

O pacote pesa 5 quilos (The package weighs 5 kilos)
- Verb *pesar* (weigh)
- Dimension: weight
- Value: 5 kg

Properties of Quantitative Relations

1. Measurement structure:

Entity measured (syntactic subject)
Dimension measured (type of measurement)
Value/quantity (numerical value + unit)

2. Verb variation by dimension:

Age, length, area: ter (have)
General measurement: medir (measure)
Cost: custar (cost)
Worth: valer (be worth)
Weight: pesar (weigh)

3. Non-volitional: Entities don't control their measurements

✗ *João decidiu ter 30 anos (João decided to be 30 years old - odd)
- Measurements are not volitional

Abstract and Attributive Relations

Definition: Relations between abstract entities, including logical implications, semantic connections, and abstract attributions.

Semantic template: ABSTRACT_RELATION(Entity₁, RelationType, Entity₂)

Portuguese realization: ter (have), implicar (imply), various relational verbs

Examples:

Implication relations:

A teoria tem implicações (The theory has implications)
- Theory: source entity
- Implicações: consequence entities
- Logical/conceptual connection

Se p, então q (If p, then q)
- Conditional relation
- Logical implication

Solution relations:

O problema tem solução (The problem has a solution)
- Problem-solution pair
- Abstract pairing relation

A questão exige resposta (The question requires an answer)
- Question-answer relation

Meaning relations:

A história tem sentido (The story has meaning)
- Story: entity with semantic content
- Sentido: meaning attributed

A palavra significa "casa" (The word means "house")
- Semantic relation between sign and referent

Causation relations (abstract):

A teoria explica o fenômeno (The theory explains the phenomenon)
- Explanatory relation
- Abstract causation

O argumento justifica a conclusão (The argument justifies the conclusion)
- Justificatory relation

Dependency relations:

O resultado depende dos dados (The result depends on the data)
- Dependency: result contingent on data
- Abstract dependence relation

Participant Structure in Relational Frames

Relational frames are characterized by their multi-participant structure - they inherently involve two or more entities in relation.

Dyadic Relations (Two Participants)

Definition: Relations involving exactly two participants standing in relation R to each other.

Structure: RELATION(x, y) where x and y are the two relatums

Most common type: The majority of relational frames are dyadic

Examples by type:

Possession (dyadic):

João tem um carro
- Participant₁: João (possessor)
- Participant₂: carro (possessed)
- Relation: possession

Kinship (dyadic):

Maria é mãe de João
- Participant₁: Maria (mother)
- Participant₂: João (child)
- Relation: motherhood

Social (dyadic):

Pedro é amigo de Ana
- Participant₁: Pedro (friend)
- Participant₂: Ana (friend)
- Relation: friendship

Part-whole (dyadic):

A roda é parte do carro
- Participant₁: roda (part)
- Participant₂: carro (whole)
- Relation: part-of

Polyadic Relations (More than Two Participants)

Definition: Relations involving three or more participants.

Structure: RELATION(x, y, z, ...) where multiple entities stand in relation

Less common than dyadic: Most relations reduce to dyadic structure

Examples:

Ternary kinship:

João apresentou Maria a Pedro (João introduced Maria to Pedro)
- Participant₁: João (introducer)
- Participant₂: Maria (introduced)
- Participant₃: Pedro (introduced to)
- Relation: introduction (ternary)

Comparative relations (ternary):

João é mais alto que Maria em relação a Pedro
(João is taller than Maria relative to Pedro)
- Participant₁: João (compared entity)
- Participant₂: Maria (comparison standard)
- Participant₃: Pedro (reference point)
- Relation: relative comparison

Exchange relations:

João trocou o livro pelo disco com Maria
(João exchanged the book for the record with Maria)
- Participant₁: João (exchanger)
- Participant₂: livro (given object)
- Participant₃: disco (received object)
- Participant₄: Maria (exchange partner)
- Relation: exchange

Note: Many apparent polyadic relations can be decomposed into multiple dyadic relations.

Symmetry, Asymmetry, and Reflexivity

Relational frames exhibit important logical properties regarding how participants relate to each other.

Symmetric Relations

Definition: Relations where R(x,y) → R(y,x) - if x relates to y, then y relates to x in the same way.

Properties:

Participants have equivalent roles
Relation holds bidirectionally
Cannot distinguish "direction" of relation

Examples:

Friendship:

João é amigo de Pedro ↔ Pedro é amigo de João
(João is friends with Pedro ↔ Pedro is friends with João)
- Symmetric: friendship goes both ways
- No asymmetry in roles

Similarity/resemblance:

Maria parece Ana ↔ Ana parece Maria
(Maria resembles Ana ↔ Ana resembles Maria)
- Symmetric: resemblance is bidirectional

Equality:

João tem a mesma idade que Maria ↔ Maria tem a mesma idade que João
(João is the same age as Maria ↔ Maria is the same age as João)
- Symmetric: equality is bidirectional

Adjacency:

A casa fica ao lado da escola ↔ A escola fica ao lado da casa
(The house is next to the school ↔ The school is next to the house)
- Symmetric: adjacency works both ways

Marriage (symmetric):

João é casado com Maria ↔ Maria é casada com João
(João is married to Maria ↔ Maria is married to João)
- Symmetric: marriage relation is mutual

Asymmetric Relations

Definition: Relations where R(x,y) does not imply R(y,x) - direction matters, and roles are distinct.

Properties:

Participants have distinct roles
Relation is directional
Reversing participants changes meaning or truth

Examples:

Possession:

João tem um carro (João has a car)
≠ O carro tem João (The car has João - nonsensical)
- Asymmetric: possessor ≠ possessed

Parent-child kinship:

João é pai de Maria (João is Maria's father)
≠ Maria é pai de João (Maria is João's father - false)
- Asymmetric: parent ≠ child
- (Though has complementary: Maria é filha de João)

Part-whole:

A roda é parte do carro (The wheel is part of the car)
≠ O carro é parte da roda (The car is part of the wheel - false)
- Asymmetric: part ≠ whole

Teacher-student:

João é professor de Maria (João is Maria's teacher)
≠ Maria é professora de João (Maria is João's teacher - false in same context)
- Asymmetric: different roles

Before/after (temporal):

Segunda vem antes de terça (Monday comes before Tuesday)
≠ Terça vem antes de segunda (Tuesday comes before Monday - false)
- Asymmetric: temporal order

Complementary Relations (Converse Relations)

Definition: Asymmetric relations that come in pairs, where R₁(x,y) ↔ R₂(y,x) - reversing participants requires changing the relation to its converse.

Properties:

Two distinct but related predicates
Describe same situation from different perspectives
Participant role reversal requires predicate change

Examples:

Kinship converses:

João é pai de Maria ↔ Maria é filha de João
(Father-of ↔ daughter-of converse pair)

Maria é avó de Pedro ↔ Pedro é neto de Maria
(Grandmother-of ↔ grandson-of converse pair)

Commercial converses:

João comprou o livro de Maria ↔ Maria vendeu o livro para João
(Buy-from ↔ sell-to converse pair)

Locational converses:

São Paulo fica ao norte de Curitiba ↔ Curitiba fica ao sul de São Paulo
(North-of ↔ south-of converse pair)

A casa fica acima da escola ↔ A escola fica abaixo da casa
(Above ↔ below converse pair)

Ownership converses:

João possui esta casa ↔ Esta casa pertence a João
(Own ↔ belong-to converse pair)

Reflexive Relations

Definition: Relations where an entity can stand in relation to itself: R(x, x) is possible.

Examples:

Self-resemblance:

João parece consigo mesmo (João resembles himself)
- Reflexive: entity can resemble itself
- Usually trivial/tautological

Self-friendship (usually odd):

? João é amigo de si mesmo (João is friends with himself)
- Pragmatically odd but logically possible

Most relations are irreflexive: Cannot hold between entity and itself

✗ João é pai de João (João is João's father - impossible)
✗ A roda é parte da roda (The wheel is part of the wheel - nonsensical)

Transitive Relations

Definition: Relations where R(x,y) AND R(y,z) → R(x,z) - if x relates to y, and y relates to z, then x relates to z.

Examples:

Part-whole (transitive):

If: O dedo é parte da mão (Finger is part of hand)
AND: A mão é parte do corpo (Hand is part of body)
Then: O dedo é parte do corpo (Finger is part of body)

Kinship (some types transitive):

If: João é pai de Maria (João is Maria's father)
AND: Maria é mãe de Pedro (Maria is Pedro's mother)
Then: João é avô de Pedro (João is Pedro's grandfather)
- Transitivity with relation change (father → grandfather)

Before/after (transitive):

If: Segunda vem antes de terça (Monday before Tuesday)
AND: Terça vem antes de quarta (Tuesday before Wednesday)
Then: Segunda vem antes de quarta (Monday before Wednesday)

Friendship (not transitive):

João é amigo de Maria (João is friends with Maria)
Maria é amiga de Pedro (Maria is friends with Pedro)
NOT necessarily: João é amigo de Pedro (João is friends with Pedro)
- Friendship is not transitive

Negation in Relational Frames

Relational frames exhibit distinctive negation patterns that differ from property negation and event negation.

Relation Negation = Absence of Relation

Principle: Negating a relation asserts that the relation does not hold between the entities (absence of connection), not that an opposite relation holds.

Contrast with property negation:

Property negation: João não é alto → João é baixo (opposite property)
Relation negation: João não tem carro → absence of possession (not: João has non-car)

Possession Negation

Affirmative:

João tem um carro (João has a car)
- Possession relation holds

Negated:

João não tem carro (João doesn't have a car)
→ Absence of possession relation
→ NOT: João possesses a non-car
→ Simply: No car is possessed by João

Characteristic: Possession negation asserts lack of the possessed entity, not possession of something else.

More examples:

Maria não tem irmãos (Maria doesn't have siblings)
→ Maria has zero siblings (absence of sibling relation)

Pedro não tem dinheiro (Pedro doesn't have money)
→ Pedro lacks money

Kinship Negation

Affirmative:

João é pai de Maria (João is Maria's father)
- Kinship relation holds

Negated:

João não é pai de Maria (João is not Maria's father)
→ Absence of fatherhood relation
→ João and Maria do not stand in father-child relation
→ NOT: João has opposite kinship to Maria

Characteristic: Kinship negation asserts absence of specific kinship tie, not presence of different kinship.

Contrast:

PROPERTY: João não é brasileiro → João é de outra nacionalidade (has different nationality)
KINSHIP: João não é pai de Maria → absence of relation (not: João is something else to Maria)

Locational Negation

Affirmative:

O livro está na mesa (The book is on the table)
- Locational relation holds: book located at table

Negated:

O livro não está na mesa (The book is not on the table)
→ Book is located elsewhere (alternative location)
→ Absence of specific location relation
→ Implies: book is in some other location

Characteristic: Locational negation asserts absence of specific location but implies entity is located somewhere else.

Locational negation implies alternative location:

If: O livro não está na mesa
Then: O livro está em algum outro lugar (The book is in some other place)
- Entities must be located somewhere
- Negation shifts location, doesn't eliminate it

Social/Professional Relation Negation

Examples:

João não é amigo de Maria (João is not Maria's friend)
→ Absence of friendship relation
→ Not: João has opposite relation (enemy)
→ Simply: no friendship bond exists

Pedro não é professor de Ana (Pedro is not Ana's teacher)
→ Absence of teaching relation
→ Not: Pedro is student of Ana
→ Simply: no teacher-student relation

Diagnostic Tests for Relational Frames

How do we identify relational frames and distinguish them from other types? Here are systematic diagnostic tests:

Test 1: Minimal Arity (Number of Participants)

Principle: Relational frames require at least two participants (minimally dyadic).

Test: Can the predicate occur with only one participant?

Relational (requires two):

✗ *João tem (João has - missing possessed object)
✗ *Maria é amiga (Maria is friends - missing friend)
✗ *A roda é parte (The wheel is part - missing whole)
- Ungrammatical or incomplete without second participant

Non-relational (can have one):

✓ João corre (João runs - monadic, one participant)
✓ Maria é alta (Maria is tall - monadic property)
✓ Pedro chegou (Pedro arrived - monadic event)

Diagnostic result: If requires at least two participants → RELATIONAL

Test 2: Participant Role Differentiation

Principle: Relational frames assign distinct roles to participants (even if symmetric, roles are marked).

Test: Can participants swap positions without changing meaning?

Asymmetric relational (roles differ):

João tem um carro (João has a car)
≠ O carro tem João (The car has João - role swap changes meaning)
- Roles: possessor ≠ possessed

Symmetric relational (roles equivalent but marked):

João é amigo de Pedro ≈ Pedro é amigo de João
(Same meaning, roles are equivalent)
- But participants still distinguished
- Relation requires both participants

Non-relational:

João corre (João runs)
- Only one participant role
- No role differentiation

Diagnostic result: If participants have distinct or marked roles → RELATIONAL

Test 3: Cannot Be Satisfied by Single Entity Alone

Principle: Relational predicates cannot be true of an entity in isolation - they require relation to another entity.

Test: Is the predicate meaningful for entity in isolation?

Relational (requires other entity):

✗ João tem ??? (João has - what? Needs possessed entity)
✗ Maria é amiga de ??? (Maria is friends with - whom? Needs friend)
✗ A roda é parte de ??? (The wheel is part of - what? Needs whole)
- Cannot be satisfied in isolation

Non-relational (can be satisfied alone):

✓ João é alto (João is tall - property of João alone)
✓ Maria corre (Maria runs - event involving Maria alone)
✓ Pedro existe (Pedro exists - monadic)

Diagnostic result: If cannot be satisfied by single entity → RELATIONAL

Test 4: Converse Test

Principle: Many relational frames have converse predicates that express the same relation from opposite perspective.

Test: Is there a converse predicate that expresses same situation?

Relational (has converse):

João é pai de Maria ↔ Maria é filha de João
(Father-of ↔ daughter-of: converse pair)

João comprou de Maria ↔ Maria vendeu para João
(Buy-from ↔ sell-to: converse pair)

Non-relational (no converse):

João corre (João runs - no converse)
Maria é alta (Maria is tall - no converse)

Note: Symmetric relations are their own converses

João é amigo de Maria ↔ Maria é amiga de João
(Friendship: self-converse)

Diagnostic result: If has converse predicate → RELATIONAL

Test 5: Symmetry Test

Principle: Some relations are symmetric (hold in both directions), others asymmetric.

Test: Does R(x,y) imply R(y,x)?

Symmetric relational:

João é amigo de Pedro → Pedro é amigo de João
(Symmetric: friendship bidirectional)

A casa fica ao lado da escola → A escola fica ao lado da casa
(Symmetric: adjacency bidirectional)

Asymmetric relational:

João é pai de Maria ≠ Maria é pai de João
(Asymmetric: parenthood directional)

A roda é parte do carro ≠ O carro é parte da roda
(Asymmetric: part-of directional)

Non-relational (test not applicable):

João corre (not relational - test doesn't apply)

Diagnostic result:

If symmetric or asymmetric → RELATIONAL
If test not applicable → NOT RELATIONAL

Test 6: Transitivity Test

Principle: Some relations are transitive (chain through intermediate entity).

Test: If R(x,y) and R(y,z), does R(x,z) follow?

Transitive relational:

If: O dedo é parte da mão AND A mão é parte do corpo
Then: O dedo é parte do corpo
- Transitive: part-of chains through intermediate

Intransitive relational:

If: João é amigo de Maria AND Maria é amiga de Pedro
NOT necessarily: João é amigo de Pedro
- Intransitive: friendship doesn't chain

Non-relational (test not applicable):

João corre (not relational - test doesn't apply)

Diagnostic result:

If transitive or intransitive → RELATIONAL
If test not applicable → NOT RELATIONAL

Test 7: Relational Noun Test

Principle: Relational predicates often have corresponding relational nouns that name the relation.

Test: Is there a noun form that names the relation?

Relational (has relational noun):

João é amigo de Pedro → amizade (friendship - relational noun)
João é pai de Maria → paternidade (fatherhood/parenthood)
A roda é parte do carro → relação parte-todo (part-whole relation)

Non-relational (no relational noun):

João corre → ? (no relational noun, "corrida" is event noun)
Maria é alta → ? (no relational noun, "altura" is property noun)

Diagnostic result: If has relational noun → RELATIONAL

Boundary Cases and Overlaps

Relational frames can overlap or be confused with other namespace types. Here we clarify the boundaries.

Relational vs. Stative Property

Overlap: Both are stative (no change), but relations involve multiple entities, properties involve single entity.

Stative property (monadic):

João é alto (João is tall)
- Property of João alone
- Monadic: one participant
- No relation to other entity required

Relational (dyadic):

João é mais alto que Maria (João is taller than Maria)
- Comparative: involves two entities
- Dyadic: two participants (João, Maria)
- Relation between entities

Diagnostic: Count participants

One participant → Stative property
Two or more participants → Relational

Relational vs. Locational

Overlap: Locational states are a subtype of relational - they express spatial relations.

Locational (relational subtype):

O livro está na mesa (The book is on the table)
- Spatial relation between book and table
- Dyadic: Figure (livro) and Ground (mesa)
- IS relational (location is a type of relation)

Classification: Locational frames are relational, with specific spatial content.

Distinction:

General relational: any type of relation (possession, kinship, etc.)
Locational: specifically spatial relation (location)

Recommendation: Tag locational as both relational and locational (subcategory)

Relational vs. Eventive/Process

Clear distinction: Dynamics

Relational (static):

João tem um carro (João has a car)
- Static relation: possession holds over time
- No change or process
- Stative

Eventive (dynamic):

João comprou um carro (João bought a car)
- Dynamic event: acquisition process
- Change occurs: João goes from not-having to having car
- Process with temporal structure

Diagnostic: Change test

No change, holds over time → Relational
Change or process → Eventive

Note: Some verbs can be relational or eventive depending on aspect:

RELATIONAL: João tem carro (João has a car - stative possession)
EVENTIVE: João está comprando carro (João is buying a car - dynamic acquisition)

Relational vs. Causative

Distinction: Causatives involve causation (Agent causes Event), relations involve connections between entities.

Causative:

João quebrou o vaso (João broke the vase)
- Agent (João) causes event (breaking)
- Dynamic: event occurs
- Causal structure

Relational:

João tem um vaso (João has a vase)
- Possessor (João) related to possessed (vaso)
- Static: relation holds
- No causation

Diagnostic: Causation presence

Causation central → Causative
Connection/association → Relational

Experiencer-Stimulus as Relational?

Overlap: Psychological states with Experiencer-Stimulus structure can be seen as relational.

Psychological state (relational interpretation):

João gosta de música (João likes music)
- Experiencer: João
- Stimulus: música
- Relational: liking-relation between João and music
- Static: holds over time

João sabe a resposta (João knows the answer)
- Knower: João
- Known: resposta
- Relational: knowledge-relation

Classification choice:

Can tag as Experiential namespace (psychological/epistemic content)
Can also tag as Relational (dyadic structure, experiencer-stimulus relation)

Recommendation: Tag psychological states as Experiential primary, Relational secondary (they are relational in structure but experiential in content).

Summary Table: Relational Frame Properties

Relational Type	Symmetry	Transitivity	Typical Verb/Copula	Example
Possession	Asymmetric	No	ter, possuir, ser de	João tem carro
Kinship	Varies (sym/asym)	Sometimes	ser	João é pai de Maria
Social/Professional	Varies	No (usually)	ser	Pedro é amigo de Ana
Part-whole	Asymmetric	Yes	ser parte de, ter	Roda é parte do carro
Quantitative	Asymmetric	No	ter, medir, custar	Mesa tem 2 metros
Abstract	Varies	Varies	ter, implicar	Teoria tem implicações
Locational	Asymmetric	Yes (containment)	estar, ficar	Livro está na mesa

Comprehensive Diagnostic Test Battery

Test	Relational Result	Non-Relational Result
Minimal arity	Requires ≥2 participants	Can have 1 participant
Role differentiation	Distinct participant roles	Single role or no roles
Isolation satisfaction	Cannot be satisfied alone	Can be satisfied alone
Converse existence	Has converse predicate	No converse
Symmetry	Symmetric or asymmetric	Test not applicable
Transitivity	Transitive or intransitive	Test not applicable
Relational noun	Has relational noun	No relational noun
Stativity	Static (like statives)	May be dynamic